QSG-String - Time as Existence - QSG State as Fundamental Mathematics v3

Main paper + Rigorous proofs: Two papers build Quantum State Geometry (QSG).If quantum states have positive curvature, they have distance. Energy spread gives a clock from that distance.Among all quantum spaces, one holds the most information: CP3. We call it the minimal atom of existence. One step up, CP4 splits naturally into 4D spacetime (from twistor theory) plus 4D internal space for spin, phase, and scale.Time direction appears because quantum phase flow flips one direction from space-like to time-like. Gravity appears because nature tries to keep information sharp — that Fisher equilibrium gives Einstein's equations. Black hole entropy A/4 comes out automatically, fixing a smallest length 2.56× Planck length, with no free parameters.The theory is testable: high-energy light should arrive slightly late, with delay growing as energy squared. LHAASO (2027-28), CTA (2028-30), and IceCube-Gen2 (early 2030s) can see it or rule it out by 2035. v2: Single PDF containing both Part I (main) and Part II (rigorous derivations of signature and Einstein-Fisher equations).